Question

A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. Fill in the blanks to create an equation for the volume of the prism as a function of the height.

Answer 1

An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

• We are given a rectangular prism.
• A rectangular prism is no different than a cuboid.
• Let the height of the rectangular prism be "h".
• The length of the rectangular prism is "h-3".
• The width of the rectangular prism is "h+5".
• The volume of the rectangular prism is the same as that of the cuboid.
• The volume of the rectangular prism is the product of its length, its width, and its height.
• The volume of the rectangular prism is (h - 3)*(h + 5)*h.
• An equation for the volume of the prism as a function of the height is :
• Volume = (h - 3)*(h + 5)*h
• Volume = (h² + 2h - 15)*h
• Volume = h³ + 2h² - 15h

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